# Solution - Trigonometric Identities

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ConceptTrigonometric Identities

#### Question

If cosθ + sinθ = √2 cosθ, show that cosθ – sinθ = √2 sinθ.

#### Solution

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Prove the following identities:

(i) (sinθ + cosecθ)^2 + (cosθ + secθ)^2 = 7 + tan^2 θ + cot^2 θ

(ii) (sinθ + secθ)^2 + (cosθ + cosecθ)^2 = (1 + secθ cosecθ)^2

(iii) sec^4 θ– sec^2 θ = tan^4 θ + tan^2 θ

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(sin ^2 63^@ + sin^2 27^@)/(cos^2 17^@+cos^@73^@)

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